Question

How to write standard form of the equation circle with a center of (-1,4);circumference 6pie?

Answer 1

`(x+1)^2+(y-4)^2=9`

Explanation:

`"the equation of a circle in standard form is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))`

`"where "(a,b)" are the coordinates of the centre and r is"`
`"the radius"`

`"we have the centre but require to find r"`

`"circumference "=2pir=6pi`

`rArrr=(6pi)/(2pi)=3`

`rArr(x+1)^2+(y-4)^2=9larrcolor(red)"equation of circle"`